Problem: Reduce to lowest terms: $- \dfrac{5}{3} \div - \dfrac{7}{6} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{7}{6}$ is $- \dfrac{6}{7}$ Therefore: $ - \dfrac{5}{3} \div - \dfrac{7}{6} = - \dfrac{5}{3} \times - \dfrac{6}{7} $ $ \phantom{- \dfrac{5}{3} \times - \dfrac{6}{7}} = \dfrac{-5 \times -6}{3 \times 7} $ $ \phantom{- \dfrac{5}{3} \times - \dfrac{6}{7}} = \dfrac{30}{21} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{30}{21} = \dfrac{30 \div 3}{21 \div 3} = \dfrac{10}{7} $